当函数y=sinx+根号3cosx,x∈R取最大值时,求自变量x的取值集合S
问题描述：
当函数y=sinx+根号3cosx,x∈R取最大值时,求自变量x的取值集合S
答
y=2(sinx*1/2+cosx*√3/2)
=2(sinxcosπ/3+cosxsinπ/3)
=2sin(x+π/3)
所以最大则x+π/3=2kπ+π/2
所以S={x|x=2kπ+π/6,k∈Z}